(2) If the path difference x = (2n + 1) пЃ¬/2 where n = 0, 1, 2. (1) If the path difference x = n пЃ¬ where n = 0, 1, 2, 3, 4 etc., constructive interference takes place and the film appears bright Therefore, the correct path difference in this case, x пЂЅ 2 пЃ t cos r пЂ It has been established on the basis of electromagnetic theory that, when light is reflected from the surface of an optically denser medium (air-medium interface) a phase change пЃ° equivalent to a path difference пЃ¬/2 occurs. This equation (i), in the case of reflected light does not represent the correct path difference but only the apparent. Or PM пЂЅ AP cos r пЂЅ ( AE пЂ« EP ) cos r пЃ‘ AE пЂЅ EP пЂЅ t пЃњ PM пЂЅ 2 t cos r X пЂЅ пЃ PM пЂЅ 2 пЃ t cos r X пЂЅ пЃ пЂЁ AB пЂ« CB пЂ CM пЂ© пЂЅ пЃ пЂЁPC пЂ CM пЂ© пЂЅ пЃ пЂЁPM пЂ© PM AP пЂЅ 2t AP пЃњ X пЂЅ 2пЃ t cos r cos r пЂЅ Sin i sin r AN / AC NA пЂЅ пЂЅ MC / AC MC пЃњ AN пЂЅ MC. Also produce CB to meet A E p r o d u c e d a t P. The angle of incidence is i and the angle of refraction is r. Draw CN normal to AT and AM normal to BC. The difference in path between the two rays AT and CQ can be calculated. At B part of it is reflected along BC and finally emerges out along CQ.

A ray SA incident on the upper surface of the film is partly reflected along AT and partly reflected along AB. It has been observed that interference in the case of thin film takes place due to (1) reflected light and (2) transmitted light.ДЎ4- INTERFERENCE DUE TO REFLECTED LIGHT (THIN FILMS) Consider a transparent film of thickness t and refractive index Вµ. Young was able to explain the phenomenon on the basis of interference between light reflected from the top and the bottom surface of a thin film.

Newton was able to show the interference rings when a convex lens was placed on a plane glass-plate. Hooke observed such colours in thin films of mica and similar thin transparent plates. Everyone is familiar with the beautiful colours produced by a thin film of oil on the surface of water and also by the thin film of a soap bubble. 13- INTERFERENCE IN THIN FILMS Newton and Hooke observed and developed the interference phenomenon due to multiple reflections from the surface of thin transparent materials.

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